There are many steps involved in the typical manufacturing process of semiconductor wafers. For example, the typical incoming wafer (e.g., bare silicon wafer) starts with a deposition of an insulating layer (i.e., a dielectric film, such as glass). After that, a layer of a pattern mask is laid down on the insulating layer using lithography. Then, materials are selectively removed from these layers using etching. After that, the photoresist mask is removed (i.e., strip) and the residues and particles are removed (i.e., clean or polish). Finally, conducting material is deposited (i.e., deposition) for each semiconductor device of the wafer. In short, the simplified and typical steps include deposition, lithography, etch, strip, clean, and deposition. Of course, frequently, many of these steps are repeated to form multiple layers.
It is common for a sample of the manufactured wafers to be measured and examined after one or more of these steps to confirm that it falls within an acceptable range of post-step error or non-uniformity. In order to quickly identify and correlate any post-step error or non-uniformity, the system tracks various operating variables (e.g., event timing, gas pressure, concentrations, temperatures, etc.) during the manufacturing process.
To help a user see any post-step error or non-uniformity of a wafer, conventional approaches utilize a colorful graphical depiction of the wafer condition (i.e., wafer map). More particularly, the conventional approaches generate the wafer map based upon a limited set of data points on the wafer itself. This is so because the wafer measurements may be time-consuming. For example, using an atomic force microscope or scanning electron microscope just a few measurements (e.g., perhaps a dozen) of a single wafer consume ten to twenty minutes.
Using this limited set of data points, the conventional approach uses spline interpolation (i.e., spline method) to predict/estimate values between measured data points. Starting from the center of the circular wafer, the spline calculations move outward radially in a manner to fit the measured data points as best as possible.